Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 3.9s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ y \cdot \left(x \cdot 3\right) - z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* y (* x 3.0)) z))

C

assert(x < y);
double code(double x, double y, double z) {
	return (y * (x * 3.0)) - z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y * (x * 3.0d0)) - z
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	return (y * (x * 3.0)) - z;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return (y * (x * 3.0)) - z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(Float64(y * Float64(x * 3.0)) - z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = (y * (x * 3.0)) - z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Final simplification 99.8%

   \[\leadsto y \cdot \left(x \cdot 3\right) - z \]

Alternative 2: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51} \lor \neg \left(y \leq 2.3 \cdot 10^{-16} \lor \neg \left(y \leq 2400\right) \land \left(y \leq 7.5 \cdot 10^{+77} \lor \neg \left(y \leq 4.1 \cdot 10^{+107}\right) \land y \leq 8.8 \cdot 10^{+134}\right)\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+51)
         (not
          (or (<= y 2.3e-16)
              (and (not (<= y 2400.0))
                   (or (<= y 7.5e+77)
                       (and (not (<= y 4.1e+107)) (<= y 8.8e+134)))))))
   (* 3.0 (* x y))
   (- z)))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+51) || !((y <= 2.3e-16) || (!(y <= 2400.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 8.8e+134)))))) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.5d+51)) .or. (.not. (y <= 2.3d-16) .or. (.not. (y <= 2400.0d0)) .and. (y <= 7.5d+77) .or. (.not. (y <= 4.1d+107)) .and. (y <= 8.8d+134))) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+51) || !((y <= 2.3e-16) || (!(y <= 2400.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 8.8e+134)))))) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+51) or not ((y <= 2.3e-16) or (not (y <= 2400.0) and ((y <= 7.5e+77) or (not (y <= 4.1e+107) and (y <= 8.8e+134))))):
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+51) || !((y <= 2.3e-16) || (!(y <= 2400.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 8.8e+134))))))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e+51) || ~(((y <= 2.3e-16) || (~((y <= 2400.0)) && ((y <= 7.5e+77) || (~((y <= 4.1e+107)) && (y <= 8.8e+134)))))))
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+51], N[Not[Or[LessEqual[y, 2.3e-16], And[N[Not[LessEqual[y, 2400.0]], $MachinePrecision], Or[LessEqual[y, 7.5e+77], And[N[Not[LessEqual[y, 4.1e+107]], $MachinePrecision], LessEqual[y, 8.8e+134]]]]]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e51 or 2.2999999999999999e-16 < y < 2400 or 7.49999999999999955e77 < y < 4.0999999999999999e107 or 8.8e134 < y

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]

   2. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} - z \]

   3. Taylor expanded in y around inf 74.4%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} \]

   if -1.5e51 < y < 2.2999999999999999e-16 or 2400 < y < 7.49999999999999955e77 or 4.0999999999999999e107 < y < 8.8e134

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. mul-1-neg 77.3%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51} \lor \neg \left(y \leq 2.3 \cdot 10^{-16} \lor \neg \left(y \leq 2400\right) \land \left(y \leq 7.5 \cdot 10^{+77} \lor \neg \left(y \leq 4.1 \cdot 10^{+107}\right) \land y \leq 8.8 \cdot 10^{+134}\right)\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-16} \lor \neg \left(y \leq 3000\right) \land \left(y \leq 7.5 \cdot 10^{+77} \lor \neg \left(y \leq 4.1 \cdot 10^{+107}\right) \land y \leq 1.32 \cdot 10^{+135}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+54)
   (* 3.0 (* x y))
   (if (or (<= y 1.4e-16)
           (and (not (<= y 3000.0))
                (or (<= y 7.5e+77)
                    (and (not (<= y 4.1e+107)) (<= y 1.32e+135)))))
     (- z)
     (* y (* x 3.0)))))

C

assert(x < y);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+54) {
		tmp = 3.0 * (x * y);
	} else if ((y <= 1.4e-16) || (!(y <= 3000.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 1.32e+135))))) {
		tmp = -z;
	} else {
		tmp = y * (x * 3.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+54)) then
        tmp = 3.0d0 * (x * y)
    else if ((y <= 1.4d-16) .or. (.not. (y <= 3000.0d0)) .and. (y <= 7.5d+77) .or. (.not. (y <= 4.1d+107)) .and. (y <= 1.32d+135)) then
        tmp = -z
    else
        tmp = y * (x * 3.0d0)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+54) {
		tmp = 3.0 * (x * y);
	} else if ((y <= 1.4e-16) || (!(y <= 3000.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 1.32e+135))))) {
		tmp = -z;
	} else {
		tmp = y * (x * 3.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	tmp = 0
	if y <= -1.9e+54:
		tmp = 3.0 * (x * y)
	elif (y <= 1.4e-16) or (not (y <= 3000.0) and ((y <= 7.5e+77) or (not (y <= 4.1e+107) and (y <= 1.32e+135)))):
		tmp = -z
	else:
		tmp = y * (x * 3.0)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+54)
		tmp = Float64(3.0 * Float64(x * y));
	elseif ((y <= 1.4e-16) || (!(y <= 3000.0) && ((y <= 7.5e+77) || (!(y <= 4.1e+107) && (y <= 1.32e+135)))))
		tmp = Float64(-z);
	else
		tmp = Float64(y * Float64(x * 3.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+54)
		tmp = 3.0 * (x * y);
	elseif ((y <= 1.4e-16) || (~((y <= 3000.0)) && ((y <= 7.5e+77) || (~((y <= 4.1e+107)) && (y <= 1.32e+135)))))
		tmp = -z;
	else
		tmp = y * (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1.9e+54], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.4e-16], And[N[Not[LessEqual[y, 3000.0]], $MachinePrecision], Or[LessEqual[y, 7.5e+77], And[N[Not[LessEqual[y, 4.1e+107]], $MachinePrecision], LessEqual[y, 1.32e+135]]]]], (-z), N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e54

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]

   2. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} - z \]

   3. Taylor expanded in y around inf 60.7%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} \]

   if -1.9000000000000001e54 < y < 1.4000000000000001e-16 or 3e3 < y < 7.49999999999999955e77 or 4.0999999999999999e107 < y < 1.32e135

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. mul-1-neg 77.3%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{-z} \]

   if 1.4000000000000001e-16 < y < 3e3 or 7.49999999999999955e77 < y < 4.0999999999999999e107 or 1.32e135 < y

   1. Initial program 99.7%

      \[\left(x \cdot 3\right) \cdot y - z \]

   2. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} - z \]
   3. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 3} - z \]

      2. fma-neg 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot x, 3, -z\right)} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot x, 3, -z\right)} \]

   5. Taylor expanded in y around inf 89.8%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative 89.8%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 3} \]

      2. associate-*r* 89.9%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 3\right)} \]

      3. *-commutative 89.9%

         \[\leadsto y \cdot \color{blue}{\left(3 \cdot x\right)} \]

   7. Simplified 89.9%

      \[\leadsto \color{blue}{y \cdot \left(3 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-16} \lor \neg \left(y \leq 3000\right) \land \left(y \leq 7.5 \cdot 10^{+77} \lor \neg \left(y \leq 4.1 \cdot 10^{+107}\right) \land y \leq 1.32 \cdot 10^{+135}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ 3 \cdot \left(x \cdot y\right) - z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* 3.0 (* x y)) z))

C

assert(x < y);
double code(double x, double y, double z) {
	return (3.0 * (x * y)) - z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (3.0d0 * (x * y)) - z
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	return (3.0 * (x * y)) - z;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return (3.0 * (x * y)) - z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(Float64(3.0 * Float64(x * y)) - z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = (3.0 * (x * y)) - z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Taylor expanded in x around 0 99.8%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} - z \]

3. Final simplification 99.8%

   \[\leadsto 3 \cdot \left(x \cdot y\right) - z \]

Alternative 5: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

assert(x < y);
double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Step-by-step derivation

   1. associate-*l* 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z \]

   2. fma-neg 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3 \cdot y, -z\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3 \cdot y, -z\right)} \]
4. Step-by-step derivation

   1. fma-neg 99.9%

      \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]

5. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right) - z} \]

6. Final simplification 99.9%

   \[\leadsto x \cdot \left(3 \cdot y\right) - z \]

Alternative 6: 50.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ -z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- z))

C

assert(x < y);
double code(double x, double y, double z) {
	return -z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -z
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	return -z;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return -z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return Float64(-z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = -z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := (-z)

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]

2. Taylor expanded in x around 0 57.1%

   \[\leadsto \color{blue}{-1 \cdot z} \]
3. Step-by-step derivation

   1. mul-1-neg 57.1%

      \[\leadsto \color{blue}{-z} \]

4. Simplified 57.1%

   \[\leadsto \color{blue}{-z} \]

5. Final simplification 57.1%

   \[\leadsto -z \]

Alternative 7: 2.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ z \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 z)

C

assert(x < y);
double code(double x, double y, double z) {
	return z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

assert x < y;
public static double code(double x, double y, double z) {
	return z;
}

Python

[x, y] = sort([x, y])
def code(x, y, z):
	return z

Julia

x, y = sort([x, y])
function code(x, y, z)
	return z
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot 3\right)} - z \]

   2. associate-*r* 99.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 3} - z \]

   3. fma-neg 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot x, 3, -z\right)} \]

   4. add-sqr-sqrt 44.3%

      \[\leadsto \mathsf{fma}\left(y \cdot x, 3, \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right) \]

   5. sqrt-unprod 53.9%

      \[\leadsto \mathsf{fma}\left(y \cdot x, 3, \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right) \]

   6. sqr-neg 53.9%

      \[\leadsto \mathsf{fma}\left(y \cdot x, 3, \sqrt{\color{blue}{z \cdot z}}\right) \]

   7. sqrt-unprod 23.8%

      \[\leadsto \mathsf{fma}\left(y \cdot x, 3, \color{blue}{\sqrt{z} \cdot \sqrt{z}}\right) \]

   8. add-sqr-sqrt 43.3%

      \[\leadsto \mathsf{fma}\left(y \cdot x, 3, \color{blue}{z}\right) \]

3. Applied egg-rr 43.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot x, 3, z\right)} \]

4. Taylor expanded in y around 0 2.1%

   \[\leadsto \color{blue}{z} \]

5. Final simplification 2.1%

   \[\leadsto z \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (3.0d0 * y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))